Answer :
Question:- Find the Value of a
Equation:-
[tex] ({x}^{2} + 5x + a)(4 {x}^{2} - 7x + a) = 0 \\ [/tex]
Given :- product of roots = 1
Answer :- 4 and 1
Explanation:-
[tex]({x}^{2} + 5x + a)(4 {x}^{2} - 7x + a) = 0 \\ [/tex]
First part:-
[tex]{x}^{2} + 5x + a = 0\\ ax²+bx+c\\a=1, c= a \\ product \: of \: root = \frac{c}{ a} = 1 \\ product \: of \: root = \frac{a}{ 1 } = 1 \\ a = 1\\ [/tex]
Second part :-
[tex](4 {x}^{2} - 7x + a) = 0\\ ax²+bx+c\\ a= 4 , c= a \\ product \: of \: root = \frac{c}{ a} = 1 \\ product \: of \: root = \frac{a}{ 4} = 1 \\ a = 4 [/tex]
Values of a is :- 1 and 4